Expanding brackets

Learning Objective:

• we are learning to expand a simple algebraic expression involving a single bracket
• by the end of this lesson you will be able to convince me that 3(2x + 5) = 6x + 15 for all values of x.

Investing:

• Think of a whole number;
• Write it down and below it write the next four whole numbers that follow it;
• Add them up;
• How quickly can you get the answer?
• Can you find a shortcut?

• Start with 13
• Write down this:

• How quickly can you tell me the answer?

Preparing:

• Are we ready? Can you already... ?
• Let's be sure you can...
• Before you start you need to know:
• You will have a deeper understanding if you also know:

Discovering:

• Can you figure it out yourself from these examples?
• Try to predict the next one aloud or on a mini-whiteboard.
• Investigate...

Modeling:

• Here are some examples of people getting it right:
• Here are some examples of people getting it wrong in typical ways:
• Here are some more examples. Did they get it right or wrong? Explain how you know!

Discussing:

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Explaining:

• One way to do this is...
• Another approach might be...
• A useful shortcut is to...
• This works because...
• It doesn't work when...
• An exception is...
• Watch out for...
• A common mistake is...
• You can check your result by...
• We can prove this works by...

Practicing:

• Some straightforward examples.
• Some harder examples.
• Some mixed examples.
• Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
• You can demonstrate fluency by at least...

Sharing:

• A web page or wiki I have created to explain this can be found at...
• A presentation I have created and rehearsed looks like...
• A poster I have drawn or model I have made can be found...

Assessing:

• Check you've mastered this skill by...
• Show you understand by explaining...
• Prove you're an expert in... by...

Developing:

• Next we could learn...
• This leads to...
• Now try...